John,

On 12 Sep 2009, at 17:01, John Mikes wrote:

> Bruno,
> the more I read here on the "Church thesis" the less I know about it.
> Is there a short description in 'non-technical' words about the  
> 'essence' you hold instrumental in the applications you apply?

I will explain in detail Church thesis after the explanation of Cantor  
and Kleene's results. If there are still problems, please ask at that  
moment. Just now would be slightly premature and confusing I think.

In a nutshell, Church thesis is the statement that "lambda calculus",  
or any of the many provably equivalent formal systems,  provides a  
correct and complete description of the notion of computability.
A provably weaker statement of Church thesis is the affirmation of the  
(mathematical) existence of universal machine. The mathematical  
existence of the UD is a direct consequence of CT.

Best,

Bruno




http://iridia.ulb.ac.be/~marchal/




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